Abstract

In recent years, the doubly geometric process is started to use as a model to fit the data from a series of events since it provides a more flexible model for wider application than the geometric process. In the applications of the doubly geometric process, the estimation problem associated with the process can arise. In this study, we deal with this problem for the stochastic process model determined by doubly geometric process when the distribution of the first interarrival time is assumed to be Weibull. The model parameters of the doubly geometric process and the parameters of Weibull distribution are estimated by using the maximum likelihood method. The joint asymptotic distribution of the estimators is obtained. We investigate some statistical properties of the estimators such as asymptotic unbiasedness and consistency. The proposed estimators are evaluated through a computer simulation study with different parameter values and sample sizes. Two goodness-of-fitness tests are applied to show that the Weibull distribution may be used for the two real world data sets which can be modeled by doubly geometric process. Finally, we present the estimators of the model and distribution parameters for these data sets.

摘要

近年来，双几何过程开始作为模型来拟合一系列事件的数据，因为它为比几何过程更广泛的应用提供了更灵活的模型。在双重几何过程的应用中，可能会出现与该过程相关的估计问题。在本研究中，我们针对由双重几何过程确定的随机过程模型处理这个问题，当第一个到达间隔时间的分布假设为 Weibull 时。采用最大似然法估计对偶几何过程的模型参数和Weibull分布的参数。获得了估计量的联合渐近分布。我们研究了估计量的一些统计特性，例如渐近无偏性和一致性。建议的估计器通过具有不同参数值和样本大小的计算机模拟研究进行评估。应用了两个拟合优度检验来表明 Weibull 分布可用于两个可以通过双几何过程建模的真实世界数据集。最后，我们介绍了这些数据集的模型和分布参数的估计量。